Question

Solve each of the following systems by the Method of Elimination. In each case you will likely want to alter both equations by multiplication.

(a) 2x+3y=16
4x+2y=30

(b) 2x+3y=17
5x+6y=32

Answer 1

a) x= 29/4 and y = 1/2.

b) x= -2 and y = 7.

Explanation:

a) explanation:

Multiply the first equation by -2,and multiply the second equation by 1.

They become: −4x−6y=−32 and 4x+2y=30

Add these equations to eliminate x:

−4y=−2

Then solve−4y=−2for y:

Divide both sides by -4.

y = -1/2.

Now that we've found y let's plug it back in to solve for x.

Write down an original equation:

2x+3y=16

Substitute 1/2 for y in2x+3y=16:

2x+3(1/2)=16

2x+3/2=16

2x=29/2

x=29/4

b) explanation:

Multiply the first equation by -2,and multiply the second equation by 1.

Becomes: −4x−6y=−34 and 5x+6y=32

Add these equations to eliminate y:

x=−2

Now that we've found x let's plug it back in to solve for y.

Write down an original equation:

2x+3y=17

Substitute −2 for x in2x+3y=17:

(2)(−2)+3y=17

3y−4=17

3y−4+4=17+4 (Add 4 to both sides)

3y=21

Divide by 3.

y= 7

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